Finite Group Databasebeta

C2×#21433490 #29455413

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#21433490

Splittings

FittingC2×C59×#410 ⋊ C2
SylowC59 ⋊ C2×#3025

Subgroups

subgroupG/H
centerC2×C4#14273697
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#410C2
socleC22×C59C2×#120
hypercenterC2×#410D59
hypocenterC59C2×#3025
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#410

5086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1036292);